Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry

Chamon, Claudio; Green, Dmitry; Yang, Zhi-Cheng

doi:10.1103/physrevlett.125.067203

Cited by 19 publications

(25 citation statements)

References 17 publications

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“…x as a function of 1/L with a power-law fit of the form y = a + bL −c . Including data for the four largest system sizes, L ≥ 12, we find the best fit with a = −0.02(1), b = 3.15(2) and c = 0.472 (7), confirming the expectation Wilson loop correlator vanishes for a conventional FM phase in the thermodynamic limit at any finite transverse field. Here, we present simulation results for Wilson loop order parameter distribution ρ(P x , P y ) for model-X.…”

Section: Appendix C: Extraction Of the Vison Gapsupporting

confidence: 58%

“…In analogy to the standard Z 2 lattice gauge theory, in our model the 4-body interaction term A i is effectively generated with the term (See Ref. [7] for further details)…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Flipping the gauge spins around the loop corresponds to choosing R matrices for each s traversed, with an even number of −1 entries associated with the links visited. For each such R, there is a corresponding monomial matrix L = W R W −1 [7]. These pairs of monomial R and L matrices are such that W = L −1 W R, and thus the transformation in Eq.…”

Section: A Baseline Model With Combinatorial Gauge Symmetrymentioning

confidence: 99%

“…Recently, a construction for which the Z 2 gauge symmetry is exact was proposed on a variant of the transverse field Ising model (TFIM), utilizing only simple two-body ferromagnetic and antiferromagnetic ZZ interactions [7]. Monomial (matrix) transformations that correspond to combinations of spin flips and permutations play a central role in the construction, thus dubbed combinatorial gauge symmetry.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we present a quantitative and detailed study of the combinatorial Z 2 gauge model originally proposed in Ref. 7. Two different types of quantum fluctuations are introduced while preserving the gauge symmetry: a transverse field acting on the gauge spins and a XX ferromagnetic interaction between the gauge spins, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry

Wu,

Yang,

Green

et al. 2021

Preprint

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We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first-order, in contrast to the conventional Z2 lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic XX interaction while keeping the local gauge symmetry intact. We find that the Z2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first-order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.

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Section: Appendix C: Extraction Of the Vison Gapsupporting

confidence: 58%

“…In analogy to the standard Z 2 lattice gauge theory, in our model the 4-body interaction term A i is effectively generated with the term (See Ref. [7] for further details)…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: A Baseline Model With Combinatorial Gauge Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry

Wu,

Yang,

Green

et al. 2021

Preprint

Self Cite

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Kagome qubit ice

et al. 2023

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Topological phases of spin liquids with constrained disorder can host a kinetics of fractionalized excitations. However, spin-liquid phases with distinct kinetic regimes have proven difficult to observe experimentally. Here we present a realization of kagome spin ice in the superconducting qubits of a quantum annealer, and use it to demonstrate a field-induced kinetic crossover between spin-liquid phases. Employing fine control over local magnetic fields, we show evidence of both the Ice-I phase and an unconventional field-induced Ice-II phase. In the latter, a charge-ordered yet spin-disordered topological phase, the kinetics proceeds via pair creation and annihilation of strongly correlated, charge conserving, fractionalized excitations. As these kinetic regimes have resisted characterization in other artificial spin ice realizations, our results demonstrate the utility of quantum-driven kinetics in advancing the study of topological phases of spin liquids.

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Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics

Huang

Meng

et al. 2022

Chinese Phys. B

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Recently, quantum simulation of low-dimensional lattice gauge theories (LGTs) has attracted many interests, which may improve our understanding of strongly correlated quantum many-body systems. Here, we propose an implementation to approximate ℤ2 LGT on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. By using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gauss law of the ℤ2 LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the emergent Gauss law under the strong transverse field, the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.

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Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry

Cited by 19 publications

References 17 publications

Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry

Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry

Kagome qubit ice

Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics

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